Although SCUBA and sender-based rate adaptation work in concert to effectively incorporate receiver interest into the adaptation process, the sender-based approach is fundamentally limited because it cannot accommodate receiver heterogeneity. More precisely, a particular source's data rate is the same at all receivers, but in a session with heterogeneous qualities of receiver connectivity, congestion-free operation requires the source to set its bandwidth to that of the most constrained link. Running each source at the rate of the slowest link is clearly undesirable and prevents well-connected receivers from fully exploiting their available bandwidth.
This limitation can be overcome with a layered transmission scheme [1, 17, 21, 22]. In this model each source generates a layered media stream that is striped across multiple network channels. The layers are typically cumulative, i.e., if a receiver wishes to decode layer n, it must also receive layer 1 through layer n-1, and each additional layer enhances the quality of the reconstructed signal. Thus, to maximize quality, a receiver subscribes to as many network channels as is possible without congesting the network. One approach, known as Receiver-driven Layered Multicast (RLM), is detailed in [17].
In [17], each source stripes its data in the most straightforward manner possible -- a signal layer k is mapped to the corresponding network layer k as depicted in Figure 4. But this arrangement treats each source equally; in SCUBA, we want to distinguish more important sources from less important ones and reflect this into the transmission algorithm. Fortunately, we can achieve this goal with a novel assignment of signal layers to network channels based on the source weights computed by SCUBA. Given a weight, each source determines its signal layer mapping, i.e., the assignment of each of its signal layers to the corresponding network channel. The source then transmits each of its signal layers on the network channel defined by the mapping.
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Figure 5 illustrates how signal layers are manipulated by SCUBA. The figure shows how two sources each with four signal layers are mapped onto eight possible network channels. The left-hand side of the figure shows a layer mapping that corresponds to a prioritization of source S1 over S0, while the right-hand configuration corresponds to a prioritization of S0 over S1. Thus, if SCUBA control messages indicate that source S1 has a larger average weight (i.e., higher priority) over source S0, then the layer mapping on the left would be collectively enforced by the sources. Likewise, in the reverse case, the right-hand configuration would be automatically selected.
We can further illustrate the natural fit between SCUBA and receiver-driven bandwidth adaptation by considering the process whereby an individual receiver incrementally adds network channels to its overall subscription. Suppose a receiver in the context of Figure 5(a) has initially subscribed to just one network channel. At this point, that receiver not only receives a stream of adequately low bandwidth, but this particular stream is guaranteed to originate from the session's highest priority source, in this case, S1. As the receiver subsequently increases its channel subscription, it not only increases the quality of its current flows, but also receives additional sources in priority order. Thus, when the receiver increases its subscription to two network channels, it additionally receives the low quality layer of source S1. Upon adding the third channel, it receives equivalent qualities of both sources. The fourth channel then increases the quality of the high priority stream, S1. In this way we complement a raw bandwidth adaptation mechanism like RLM with a mechanism that explicitly accounts for the relative importance of media flows across the session.
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We now formalize the algorithm for determining the signal layer mappings from the set of average weights. In addition to the notation defined earlier, we define the following quantities:
Let Rj be the transmission rate for signal layer j. Note that we assume that the rate hierarchies induced by all the media sources are homogeneous and further that each layer generates a constant bit-rate flow. Modifying our algorithm to account for heterogeneous and dynamic sources is a topic of future research. Let C be the total number of network channels available for transmission and let Lk be the bandwidth limit on the k'th network channel. We assume that:
Let Aj,n be the network channel assigned to signal layer n at source Sj.
Our notation is summarized in Table 1.
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The goal of the algorithm is to compute Aj,n -- i.e., to map signal layers onto network channels -- according to the SCUBA weights ( w1, ..., wN) while adhering to the bit-rate constraints ( L1,..., LC). In addition, the algorithm should have the property that a network channel number assigned to layer k for some source is less than or equal to any channel assigned to a layer k of any other source with equal or lower priority. In summary, we impose the following constraints on our algorithm:
One algorithm that obeys these constraints is given in Figure 6. We assume that all values for Aj,n are initially undefined and that a reference to an undefined value (line 10) is interpreted as 0 (including negative index values). tk is a ``temporary variable'' that represents the next unprocessed signal layer of source Sk. Upon completion, Aj,n contains a feasible layer mapping. A proof that our algorithm adheres to the stated constraints is given in the appendix.
